Paired proportions

Two proportions are paired (as opposed to independent) if they share a common feature that affects the outcome. For example, when comparing two laboratory methods (culture media) to detect bacteria in samples of blood, if blood from the same sample is put into both methods, this is the "pairing". Pairs of results from multiple samples can then be compared as a pair of proportions:

The data below represent a comparison of two media for culturing Mycobacterium tuberculosis. Fifty suspect sputum specimens were plated up on both media and the following results were obtained:

Medium B:

Growth

No Growth

Medium A:

Growth

20

12

No Growth

2

16

N = 50

To analyse these data in StatsDirect you must select paired proportions from the proportions section of the analysis menu. Select a 95% confidence interval by pressing enter when you are presented with the confidence interval menu. Enter TOTAL (n) as 50, BOTH (k) as 20, FIRST (r) as 12 and SECOND (s) as 2.

For this example:

Total = 50, both = 20, first only = 12, second only = 2

Proportion 1 = 0.64

Proportion 2 = 0.44

Proportion difference = 0.2

Exact two sided P = .0129

Exact one sided P = .0065

Exact two sided mid P = .0074

Exact one sided mid P = .0037

Score based (Newcombe) 95% confidence interval for the proportion difference:

0.056156 to 0.329207

Here we can conclude that the proportion difference is statistically significantly different from zero. With 95% confidence we can say that the true population value for the proportion difference lies somewhere between 0.06 and 0.33. This leaves us with little doubt that medium A is more effective than medium B for the culture of tubercle bacilli.